Let #h(t) = (2-t)/(t)# and #g(t)= (3t+15)/t#, how do you find (h/g)(t) and the domain for h/g?

1 Answer
Konstantinos Michailidis
Sep 10, 2015

We have that #(h(t))/g(t)=(2-t)/(3t+15)# and the domain of #(h(t))/g(t)# is #R-{0,-5}#

Explanation:

We have that

#(h(t))/g(t)=((2-t)/t)/((3t+15)/t)=(2-t)/(3t+15)#

The domain of #(h(t))/g(t)# is #R-{0,-5}#

The domain of a quotient is a subset of the intersection of the domains. Since neither domain contains 0, the domain of the quotient excludes 0 as well.

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